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1、<p><b>  中文4457字</b></p><p><b>  外文參考資料</b></p><p>  Mechanical properties of pervious cement concrete</p><p>  CHEN Yu1, WANG Ke-Jin2, LIANG Di1</p&

2、gt;<p>  1. School of Traffic and Transportation Engineering,</p><p>  Changsha University of Science and Technology, Changsha 410004, China;</p><p>  2.Department of Civil, Construction

3、and Environmental Engineering, Iowa State University, Ames, IA50010, USA © Central South University Press and Springer-Verlag Berlin Heidelberg 2012 </p><p>  Abstract: Compressive and flexural strength

4、, fracture energy, as well as fatigue property of pervious cement concrete with either supplementary cementitious materials (SCMs) or polymer intensified, were analyzed. Test results show that the strength development of

5、 SCM-modified pervious concrete (SPC) differs from that of polymer-intensified pervious concrete (PPC), and porosity has little effect on their strength growth. PPC has higher flexural strength and remarkably higher flex

6、ural-to-compressi</p><p>  Key words: pervious concrete; strength; fracture; fatigue life</p><p>  1 Introduction</p><p>  Pervious cement concrete was a concrete with continuous vo

7、ids that were intentionally incorporated into concrete by blending with no or very little amount of fine aggregates. Cementitious materials were not enough to fill the voids among coarse aggregates with special particle-

8、size distribution to make interconnected macro pores [1?2]. The range of porosity that was commonly reported for pervious concrete utilized in pavement, was about 15%?25% [3?4]. </p><p>  The significantly r

9、educed strength of conventional pervious concrete due to high porosity, not only limited its application in heavy traffic roads but also influenced the stability and durability of the structures, because of,for example,

10、susceptibility to frost damage and low resistance to chemicals. However, by using appropriatelyselected aggregates, silica fume (SF) or organic intensifiers, and by adjusting concrete mixing proportion, the mechanical pr

11、operties of pervious concrete could be im</p><p>  Fundamental information, including the effects of porosity, water-to-cement ratio, cement paste characteristic, volume fraction of coarse aggregates, size o

12、f coarse aggregates on pervious concrete strength, had been studied [3, 9?12]. However, for the reason that the porosity played a key role in the functional and structural performances of pervious concretes [13?14], ther

13、e was still a need to understand more about the mechanical responses of pervious concretes proportioned for desired levels o</p><p>  Although it was possible to have widely different pore structure features

14、 for a given porosity, or similar pore structure features for varied porosities in pervious concrete, it was imperative to focus on the mechanical responses of pervious concrete at different designed porosities. However,

15、 compared with the related research on conventional concrete, very limited study had been conducted on the fracture and fatigue behaviors of pervious concrete, which were especially important for pavement co</p>&

16、lt;p>  The presented work outlined the raw materials and mixing proportions to produce high-strength supplementary cementitious material (SCM) modified pervious concrete (SPC) and polymer-intensified pervious concrete

17、 (PPC) at different porosities within the range of 15%?25%. Then, the mechanical properties of pervious concrete, including the compressive and flexural strengths, fracture energy, as well as fatigue property, were inves

18、tigated in details.</p><p>  2 Experiment program</p><p>  2.1 Raw materials and mixing proportions</p><p>  Type I Ordinary Portland Cement (OPC, with the details in Table 1) and g

19、ranite aggregates were used for all pervious concrete mixtures. The combined aggregates,4.75 mm and 9.5 mm particles were chosen to prepare the mixtures. To cast SPC, fly ash (type C, FA), SF and SP were used; while SJ-6

20、01, the mixture of vinyl acetate ethylene copolymer (VAE) and acrylic emulsion, was added to produce PPC. Table 2 lists the main properties of SJ-601.</p><p>  Two series of testing specimens were cast in ac

21、cordance with the designated mixing proportions presented in Table 3, in which ψ indicates the mass ratio of aggregate in 1 m3 concrete to the loose density after being densely vibrated. The percentages of FA and SF were

22、 the replacements of the same mass of OPC; while those of SP and SJ-601 were the additional dosages. It should be clarified that too much polymer blocked the valid pores and badly influenced the permeability of pervious

23、concrete. SJ-</p><p>  2.2 Test methods</p><p>  The strength tests were carried out according to GT/B 50081 — 2002 (Standard for Test Method of Mechanical Properties in Ordinary Concrete).</

24、p><p>  Strain gauges were stick at the mid-point on the bottom surface of beam specimen (150 mm × 150 mm × 550 mm), which sustained two-thirds symmetrical loading F. The corresponding strain ξ was me

25、asured by X?Y digital recorder. ξ was then translated into , which meant the mid-span deflection of beam specimen in accordance with Eq. (1). So, the enveloped area by F?▽ curve and X-axis was defined as W, fracture ener

26、gy of concrete, which could be calculated by Eq. (2) [15?16]:</p><p><b>  (1)</b></p><p><b>  (2) </b></p><p>  Where▽is the dynamic deflection of the mid-sp

27、an beam; L and H are the span and height of beam specimen, respectively. ξ is the strain value measured at the midpoint of beam bottom, while a refers to the horizontal distance from the loading point to the support abut

28、ments.</p><p>  MTS-810 TEST STAR, an electro-hydraulic servo-type material testing machine, was served to measure the flexural fatigue life of pervious concrete. Three stress levels of sine wave loading (0.

29、90, 0.80 and 0.70) with 0.1 of cycling eigenvalue, 10 Hz of frequency and zero time gap, were adopted. The number of the cyclic load that the tested specimens were subjected until failure was recorded.</p><p&g

30、t;  3 Results and discussion</p><p>  3.1 Strength</p><p>  The compressive strengths of all mixes are expressed as a percentage of their 28 d strength and shown in Fig. 1. No evident effect of

31、porosity on the strength development for both SPC and PPC is observed, that is, pervious concretes at different porosities follow the same strength growth process. The strength development of SPC is obviously rapid at ea

32、rly ages with more than 50% at 3 d and 80% at 7 d; while the further increments are only 5.6% at 56 d and 8.9% at 90 d on average, respectively (F</p><p>  Figure 1(b) shows that the compressive strength of

33、PPC is short of 50% at 7 d and reaches only about 70% at 14 d, which quite lags behind the strength development of SPC. Cement hydration and polymer film-forming process take place at the same time. It is time consuming

34、for cement hydration products and organic films to intertwine, to interpenetrate and to build up the network structure of paste, firmly wrapping and binding aggregate particles together. Therefore, PPC obtains accelerate

35、d strengt</p><p>  Seen from Table 4, PPC has higher 28 d flexural strengths and remarkably higher flexural-to-compressive strength ratios than SPC at the same porosity level. SJ-601 intensifies pervious con

36、crete by forming strongly cohesive film at the interfacial transition zone (ITZ) between aggregates and hardened paste, and by filling the micro pores within concrete. It makes previous concrete less brittle and have str

37、onger resistance to flexural damage. Figure 2 represents that the flexuralto-compressive str</p><p>  Fig. 1 Strength development of pervious concrete: (a) SPC; (b)PPC</p><p>  Fig. 2 Flexural-t

38、o-compressive strength ratio of pervious concrete</p><p>  3.2 Fracture energy</p><p>  The mixes with similar porosity (i.e. around 19.5%), PPC3, PPC4 and SPC6, were chosen to test the fracture

39、 properties. 8% and 10% of SJ-601 were added into PPC3 and PPC4, respectively, while SPC6 had no polymer addition. The results are shown in Fig. 3.</p><p>  At the beginning of loading, the curve is approxim

40、ately a straight line, which explains that both SPC and PPC show good elasticity under low stresses. When the load is up to some extent (i.e. 17.3 kN for SPC6), the straight line in Fig. 3 becomes nonlinear at the point

41、of 94.2% of the maximum load and the curve segment is quite short, illustrating that the damage mainly belongs to brittle fracture. In contrast, the starting points on the nonlinear section are at 87.9% for PPC3 and 82.5

42、% for PPC4</p><p>  Results of fracture test are also given in Table 5. It is demonstrated that the fracture energy significantly increases with the increase of polymer dosage. The fracture energies of PPC3

43、and PPC4 are improved by 44% and 73% individually compared to that of SPC6. So,compared to SPC, PPC has much more excellent resistance to cracking and crack propagation, and needs more fracture energy to be totally destr

44、oyed. It is proved that polymer materials in pervious concrete intensify cement paste and mod</p><p>  Fig. 3 Load?deflection curves of pervious concrete with different dosages of SJ-601</p><p>

45、  Fig. 4 Different failure modes of pervious concrete: (a) Highstrength pervious concrete-PPC; (b) Low-strength pervious concrete-SPC</p><p>  3.3 Flexural fatigue property</p><p>  Two-paramete

46、r Weibull probability function [17] could be written as</p><p>  ln[ln(1/p)]=blnN-blnNa (4)</p><p>  To simplify the calculation, mathematical transformation is made:</p&g

47、t;<p>  Y=ln[ln(1/p)]-ln[ln1/(1﹣pˊ)] </p><p>  X=ln N ,α=blnNa (5) </p><p>  where p means the survival probability and p′ is thus the failure probabilit

48、y; therefore p=1?p′. N is the fatigue cycle, while b and Na are the Weibull parameters. Twice natural logarithm of both sides of Eq. (5) is rewritten as Eq. (6), which can be used to determine whether a group of test dat

49、a obeys the distribution of two-parameter Weibull probability function: </p><p>  Y=bX?α (6)</p><p>  Results from the flexural fatigue test of perviou

50、s concrete are listed in Table 6, by linear regression of which there comes Fig. 5. Linear relationships between ln[ln(1/p)] and lnN under different stress levels are observed. It is proved that two-parameter Weibull pro

51、bability function is suitable to describe the flexural fatigue life of pervious concrete. So, Eq. (4) can be rewritten as</p><p>  N=Na| ln (1 -pˊ) |1/b (7)</p><p>  Fig. 5

52、 Relationship between ln[ln(1/p)] and lnN for pervious concrete: (a) SPC; (b) PPC</p><p>  For specified failure probabilities p′, the corresponding fatigue lives are calculated and listed in Table 7. It is

53、found that PPC has longer flexural fatigue life than SPC under different failure probabilities and at all stress levels, since the macromolecule polymer helps to limit cracking and delay cracking growth. Double logarithm

54、ic equation of the fatigue life of pervious concrete is established:</p><p>  lgS=lga-clgN (8)</p><p>  where S refers to the stress level; a and c are undetermined co

55、efficients. Data in Table 7 are used for regression analysis in accordance with Eq. (8), and the results are presented in Table 8. For a given p′, the flexural fatigue equations of both SPC and PPC at porosities within t

56、he range of 15%?25% are thus obtained.</p><p>  4 Conclusions</p><p>  1) There is no obvious effect of porosity on the strength growth of pervious concrete. SPC obtains strength at early ages w

57、hile the further increments are rather low. The strength development of PPC lags behind at early ages but is accelerated at later ages due to the continuous hydration of cement and film-forming of polymer materials.</

58、p><p>  2) PPC has both higher flexural strength and obviously higher flexural-to-compressive strength ratio than SPC at the same porosity level. Their flexural-tocompressive strength ratios decrease for higher

59、 porosities, indicating that the flexural strength is quite sensitive to porosity of pervious concrete.</p><p>  3) Compared to SPC, PPC has much more excellent resistance to cracking and crack propagation f

60、or the greatly improved fracture energy. With the addition of polymer materials, pervious concrete shows some characteristics of plastic flow and good toughness.</p><p>  4) PPC has longer fatigue life than

61、SPC for any given failure probability and at any stress level. Two-parameter Weibull probability function is proved to be fit to describe the flexural fatigue of pervious concrete, and the equations for both SPC and PPC

62、are recommended.</p><p>  References</p><p>  [1] CHEN Yu, ZHANG Qi-sen, GAO Ying-li. Manufacturing technology of porous cement concrete for highway construction [J]. Road Pavement Material Char

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65、orous concrete properties [J]. Construction and Building Materials, 2008, 22(5): 894?901.</p><p>  [4] NEITHALATH N. Extracting the performance predictors of enhanced porosity concretes from electrical condu

66、ctivity spectra [J]. Cement and Concrete Research, 2007, 37(5): 796?804.</p><p>  [5] HUANG Bao-shan, WU Hao, SHU Xiang, BURDETTE E G. Laboratory evaluation of permeability and strength of polymer-modified p

67、ervious concrete [J]. Construction and Building Materials, 2010, 24(5): 818?823.</p><p>  [6] CHEN Yu. Study on high-performance porous cement concrete pavement for low traffic highway tunnel [D]. Changsha:

68、Central South University, 2007. (in Chinese)</p><p>  [7] YANG Jing, JIANG Guo-liang. Experimental study on properties of pervious concrete pavement materials [J]. Cement and Concrete Research, 2003, 33(3):

69、381?386.</p><p>  [8] KEVERN J T. Advancement of pervious concrete durability [D]. Ames, IA, USA: Iowa State University, 2008.</p><p>  [9] SCHAEFER V R, WANG K, SULIEMAN M T, KEVERN J T. Mix de

70、sign development for pervious concrete in cold weather climates [R]. Iowa Department of Transportation. National Concrete Pavement Technology Center, Iowa Concrete Paving Association. 2006.</p><p>  [10] GHA

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74、vious concretes proportioned for desired porosities and their performance prediction [J]. Cement & Concrete Composites, 2011, 33(4): 778?787.</p><p>  [14] PARK S B, SEO D S, LEE J. Studies on the sound

75、absorption characteristics of porous concrete based on the content of recycled aggregate and target void ratio [J]. Cement and Concrete Research, 2005, 35(9): 1846?1854.</p><p>  [15] LI Q S, FANG J Q, TANG

76、J. Failure probability prediction of concrete components [J]. Cement Concrete Research, 2003; 33(10): 1631?1636.</p><p>  [16] SHENG Xin-pu, HUANG Zhi-qiang, BAO Wen-bo, CHEN Si-li. Experimental study and th

77、eory on fracture of concrete [M]. Beijing: China Waterpower Press, 2008: 131?132. (in Chinese)</p><p>  [17] ZHENG Mu-lian, WANG Bing-gang. HU Chang-shun. Study of fatigue property of porous concrete [J]. Ch

78、ina Journal of Highway and Transport, 2004, 17(4): 7?11. (in Chinese)</p><p><b>  譯文</b></p><p>  透水水泥混凝土的力學性能</p><p>  陳瑜1 王科進2 梁地1</p><p>  1、交通運輸工程學院,長

79、沙理工大學,長沙410004,中國; 2、土木,建筑與環(huán)境工程,愛荷華州立大學,ia50010,美國©中南大學出版社、柏林海德堡出版社2012</p><p>  摘要: 分析透水水泥混凝土的抗壓強度、抗彎強度、 斷裂能、以及其膠凝材料 (SCMs) 的疲勞性能。測試結果表明膠凝透水混凝土(SPC) 的強度增長與聚合物透水混凝土 (PPC) 不同,并且孔隙率對其強度增長幾乎沒有影響。在孔隙率相同的條件下

80、,聚合物透水混凝土比膠凝透水混凝土具有更高的抗彎強度和明顯偏高的彎曲抗壓強度比。根據(jù)孔隙率約為19.5%的透水混凝土的斷裂試驗的結果表明,斷裂能會隨著聚合物的用量增加而增加,表現(xiàn)其韌性破壞特性而不是脆性破壞特性。在給定的任何破壞概率和應力水平條件下,聚合物透水混凝土要比膠凝透水混凝土顯示的疲勞壽命更長。它證明了威布爾概率函數(shù)所描述的透水混凝土的彎曲疲勞性能。</p><p>  關鍵詞:透水混凝土;強度;斷裂;疲

81、勞壽命</p><p><b>  1介紹 </b></p><p>  透水水泥混凝土是由骨料、水泥和水拌制而成的一種多孔輕 質混凝土,它不含細骨料,由粗骨料表面包覆一薄層水泥漿相互粘結而形成孔穴均勻分布的蜂窩狀結構,孔隙率的范圍大約為15%?25%,這種混凝土一般是用做于路面 [3?4]。</p><p>  由于高孔隙率使傳統(tǒng)透水混凝土的

82、強度顯著降低, 影響了結構的穩(wěn)定性和耐久性,所以限制了它在交通擁擠的道路的應用。但是,通過適當?shù)倪x擇骨料、硅灰(SF)或有機含硼鐵合金,調整混凝土配合比,透水混凝土的力學性能就可以大大提高[5?6]。楊景和江郭良[7]表示,在透水混凝土中使用硅灰(SF)和強塑劑(SP)可以明顯提高其強度。研究結果還表明,使用硅灰的透水混凝土的性能比使用可滲透聚合物與強塑劑的透水混凝土性能的效果要更好;并且它也可以獲得50Mpa的抗壓強度和6 Mpa彎曲

83、強度。凱文[8]提出了,在透水混凝土中添加聚合物(丁苯橡膠)能改善其和易性、強度、透氣性和耐凍融性,使水泥用量相對較低的透水混凝土擁有更高的強度和更高的孔隙率。</p><p>  目前已經(jīng)研究的內(nèi)容,包括孔隙率的影響、水灰比、水泥漿的特點、粗骨料的體積分數(shù)、粗骨料的大小對透水混凝土強度的影響[3,9?12]。然而,由于孔隙率對透水混凝土的結構性能[13?14]具有關鍵作用的,所以需要更多地了解關于透水混凝土力學

84、反應所要求的相稱的孔隙率。</p><p>  雖然有大量不同的孔隙結構特征,但是在孔隙率不同的透水混凝土里,對于一個給定的孔隙率,或類似的孔隙結構特征,必須研究透水混凝土力學反應。然而,在傳統(tǒng)的混凝土相關研究中,已經(jīng)對透水混凝土的斷裂和疲勞性能進行了非常有限的研究,其中路面混凝土受交通擁擠和季節(jié)性溫度變化的影響方面的研究是尤其重要的。</p><p>  本文概述了孔隙率范圍在15%—2

85、5%的高強度膠凝透水混凝土和聚合物透水混凝土配制所需的原材料及配合比的設計。然后, 研究了透水混凝土的力學性能,包括抗壓強度、抗彎強度、斷裂能,以及疲勞特性等性能。</p><p><b>  2實驗過程</b></p><p>  2.1原材料和配合比設計</p><p>  實驗材料:水泥為I型普通硅酸鹽水泥(OPC,具體詳情見表1)。骨料

86、為花崗巖,骨料粒徑大于4.75毫米或9.5毫米。外加劑:sj - 601、醋酸乙烯的混合乙烯共聚物(VAE)、丙烯酸乳液和強塑劑。摻合料:粉煤灰(C類、FA)、硅灰。sj- 601的主要性質見表2。</p><p>  兩種測試試樣的配合比例見表3,ψ表示每立方米的混凝土中骨料的質量比。粉煤灰和硅灰的比例被質量相同的普通硅酸鹽水泥所替代,外加劑是塑化劑和sj - 601。注意,過多的聚合物會阻塞孔隙,嚴重影響透水

87、混凝土滲透率的有效性,所以不建議sj - 601劑量超過12% [1,6]。</p><p><b>  2.2測試方法</b></p><p>  根據(jù)GT / B 50081 – 2002《普通混凝土標準的力學性能試驗方法》進行強度測試。</p><p>  應變片貼在梁試件(150 mm×150 mm×550 mm)底

88、部表面的中點,持續(xù)承受三分之二的均勻荷載F 。應變ξ用X?Y數(shù)字記錄器測量。ξ隨后轉化成▽,中跨梁的彎曲試樣依照公式(1)計算。所以,由荷載F應變曲線和x軸包圍的區(qū)域定義為W,混凝土的斷裂能,可以用公式(2) [15?16]計算:</p><p><b>  (1)</b></p><p><b>  (2)</b></p><

89、;p>  ▽是梁跨中的動態(tài)撓度,L和H分別是梁的跨度和高度。ξ是梁底中點的應變值,即裝載點到支持基水平的距離。</p><p>  測量透水混凝土的抗彎疲勞壽命的實驗儀器是MTS- 810電液伺服式材料試驗機。采用三個應力水平的正弦波加載(0.90,0.80和0.70),循環(huán)特征值為0.1,赫茲的頻率為10,時間差為0。記錄循環(huán)荷載試驗的荷載次數(shù)直到試件破壞為止。</p><p>&

90、lt;b>  3結果和討論</b></p><p><b>  3.1強度</b></p><p>  圖1可以看出,表示混合物的抗壓強度與28 d抗壓強度的比值。對于膠凝透水混凝土(SPC)和聚合物透水混凝土(PPC)而言,孔隙率不影響它們強度的增大,也就是說,不同孔隙率的透水混凝土強度的增長遵循相同的過程。顯然,膠凝透水混凝土的強度在3d后快速超

91、過50%,在7d時快速超過 80%;而在56d只增加了5.6%并且在90d增加了8.9%,分別見圖1(a)。添加硅灰和塑化劑的水泥漿硬化后覆蓋在骨料上膠結形成骨架—孔隙結構,得到更大的強度來抵抗外部荷載。混有大量骨料的透水混凝土的強度增長比普通混凝土更穩(wěn)定些。</p><p>  見圖1(b),聚合物透水混凝土的在7d時抗壓強度低于50%而在14 d時只有約70%,這在強度增長方面低于膠凝透水混凝土。水泥水化和聚

92、合物成膜過程發(fā)生在同一時間。它使得水泥水化產(chǎn)物和有機薄膜交織在一起,互相滲透并建立網(wǎng)絡結構,牢固地將骨料顆粒包裹和綁定在一起。因此,聚合物透水混凝土的后期強度發(fā)展較快,即在90d后平均為117%。值得注意的是,因為水泥水化和sj - 601聚合不一致,它有利于聚合物透水混凝土在至少3d的條件下確保連續(xù)水泥水化,然后放置在相對濕度低于70%的干燥環(huán)境形成更好的聚合物。</p><p>  與膠凝透水混凝土相比,相同

93、孔隙率的聚合物透水混凝土在28d后具有較高的彎曲強度和更高的彎曲壓縮強度比,見表4。sj-601通過填充微孔促使透水混凝土在骨料和水泥漿的界面過渡區(qū)(ITZ)之間形成粘性的薄膜。它具有較強的彎曲強度,普通混凝土與之相比顯得更加脆弱。圖2表示,隨著彎曲和抗壓強度比的降低,孔隙率反而增加,這可能要歸結于,在孔隙率方面透水混凝土的彎曲強度比其抗壓強度要更敏感。</p><p>  圖1透水混凝土強度發(fā)展:(1)SPC;

94、(2)PPC</p><p>  圖2透水混凝土彎曲壓縮強度比</p><p><b>  3.2斷裂能量</b></p><p>  與聚合物透水混凝土3(PPC3)、聚合物透水混凝土4(PPC4)和膠凝透水混凝土6(SPC6)類似的孔隙率(即約19.5%)的混合物,測試其斷裂特性。聚合物透水混凝土3添加8%的sj - 601,聚合物透水混凝

95、土4添加10%的sj - 601,而膠凝透水混凝土6無外加劑,結果見圖3。</p><p>  開始加載時,曲線大約是一條直線,這表示了膠凝透水混凝土和聚合物透水混凝土在低應力時都有良好的彈性。當荷載達到某種程度時(即膠凝透水混凝土為17.3 kN),圖3的直線在最大荷載的94.2%的時候為非線性曲線并且曲線段很短,說明其所受損傷主要屬于脆性斷裂。相比之下,非線性部分的起點在聚合物透水混凝土4的87.9%和聚合物

96、透水混凝土3的82.5%的位置。因此,可以得出結論,隨著聚合物用量的增加,透水混凝土表現(xiàn)出更好的塑性流動和良好韌性。</p><p>  斷裂測試結果見表5。結果表明,隨著聚合物用量增加斷裂能顯著的提高。與膠凝透水混凝土6相比,聚合物透水混凝土3和聚合物透水混凝土4的斷裂能量分別提高了44%和73%。因此,與膠凝透水混凝土相比,聚合物透水混凝土具有更優(yōu)良的抗裂化和裂紋擴展,所以需要更多的斷裂能才能將其破壞。這證明

97、了透水混凝土的聚合物材料加強了水泥的粘性并且改變界面過渡區(qū),導致破裂模式的改變,如圖4所示。對于聚合物透水混凝土,穿過骨料顆粒核心的斷裂模式,證明了在透水混凝土中無論是孔隙還是界面過渡區(qū)都是最薄弱的部分。</p><p>  圖3不同劑量的sj-601透水混凝土的荷載?撓度曲線</p><p>  圖 4 透水混凝土的不同破壞模式: (a) 高強度透水混凝土-PPC ;(b) 低強度透水混

98、凝土-SPC</p><p><b>  3.3彎曲疲勞性能</b></p><p>  威布爾概率函數(shù)[17]為:</p><p>  ln[ln(1/p)]=blnN-blnNa (4)

99、 </p><p>  為了簡化計算,數(shù)學轉換為:</p><p>  Y=ln[ln(1/p)]-ln[ln1/(1﹣pˊ)]</p><p>  X=ln N ,α=blnNa (5)</p>

100、<p>  其中p為有效概率,pˊ為失效概率;因此p = 1?pˊ。N是疲勞循環(huán),而b和Na都是威布爾參數(shù)。兩個雙對數(shù)方程(5)改寫為方程(6),方程(6)可以用來確定一組測試數(shù)據(jù)是否遵循威布爾分布的概率函數(shù):</p><p>  Y=bX?α (6)

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